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  • 1
    Call number: 11/M 93.0959
    In: Cambridge topics in mineral physics and chemistry
    Type of Medium: Monograph available for loan
    Pages: 229, Al S.
    ISBN: 0521384494
    Series Statement: Cambridge topics in mineral physics and chemistry 1
    Classification: A.3.6.
    Language: English
    Location: Reading room
    Branch Library: GFZ Library
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  • 2
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract The temperature dependence of the hexagonal c unit cell parameter of high-purity NaNO3 shows an anomaly at 553 K corresponding to the orientational ordering transition. The a unit cell parameter is barely influenced by the transition. The single component spontaneous strain for this zone boundary instability is large (∼55×10−3 at 295 K), and couples quadratically with the order parameter. The critical exponent β is found to have the value 0.22 ± 0.01, which differs from that expected in the classical case. Below ca 450 K, crossover to tricritical behaviour is observed (β=1/4). The temperature evolution of the macroscopic order parameter as revealed by the temperature dependence of the spontaneous strain follows a tricritical behaviour between 70 K and 450 K. At temperatures below 70 K order parameter saturation is observed. Combined with recent data from specific heat measurements, the critical exponents suggest that the three-dimensional, three-states Potts model may describe the transition. Precursor spontaneous strain above T c is consistent with local ordering and may result from fluctuations associated with an antiordered NO3 group pair configuration.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract Hard mode Raman Spectroscopy and optical birefringence studies have been used to evaluate the temperature behaviour of order parameters for the cubictetragonal phase transition in leucite. There is a strong temperature-dependence of Raman line frequencies near 498 cm−1 and 529 cm−1, and the optical birefringence decreases towards zero on heating. Above the transition temperature leucite still shows slight birefringence, which correlates with the persistence of the 200 X-ray reflexion at these temperatures, and is not compatible with the ideal cubic symmetry. Quantitative observations of the temperature evolution of Raman line-frequencies and the birefringence are consistent with an order parameter showing T 1g symmetry, and a nearly-tricritical phase transition behaviour. The results of earlier X-ray and DSC studies imply the operation of an additional order parameter, with E g symmetry; this is observed, but its influence on the transition behaviour is significant only at temperatures close to T c. The two order parameters are related via linear-quadratic or biquadratic coupling. We develop the form of the Landau Potential for leucite — including both order parameters and their couplings — to discuss the present observations and previous structural data.
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  • 4
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract The structural phase transition in titanite is correlated with a strong temperature dependence of Raman scattering cross sections and, to a somewhat lesser extent, with shifts of the phonon frequencies. Their quantitative temperature evolution in the low-symmetry phase (P21/a) is compatible with a nearly 2D Ising behaviour with β≈0.12 and T c = 497 K. At temperatures above 860 K, the phonon signals agree with A 2/a symmetry but not in the temperature interval between 497 K and 860 K. In this temperature range new structural states give rise to additional phonon signals. A model based on mobile APBs between slabs of P21/a material, first proposed by van Heurck et al. (1991), is in qualitative agreement with our experimental observations.
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  • 5
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract The orientational ordering transition R $$R\bar 3m - R\bar 3c$$ in NaNO3 near 552 K has been investigated using x-ray diffraction techniques. NaNO3 is a model system for CaCO3 and other minerals with orientational disorder of triangular molecules in a simple NaCl-type matrix. The temperature evolution of the integrated intensities of the superlattice reflection $$\bar 1$$ 23 and the fundamental reflection 110 are discussed in terms of Landau theory of two coupled order parameters. It is shown that the known phenomenological critical exponent (Poon and Salje 1988) and the anomalous thermal expansion at T 〉 T tr (Reeder et al. 1988) can be understood as the result of a Z point instability which mainly describes the NO 3 - disorder, and a second order parameter linked with the spontaneous strain of this phase transition.
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  • 6
    Electronic Resource
    Electronic Resource
    Copenhagen : International Union of Crystallography (IUCr)
    Acta crystallographica 56 (2000), S. 947-952 
    ISSN: 1600-5740
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The crystal structure of a radiation-damaged natural zircon, ZrSiO_{4} (\alpha-decay radiation dose is ca 1.8 × 10^{18} α-decay events g−1), has been determined. The anisotropic unit-cell swelling observed in the early stages of the amorphization process (0.17% along the a axis and 0.62% along the c axis compared with the undamaged material) is a consequence of the anisotropy of the expansion of ZrO_{8} polyhedra. Larger anisotropic displacement parameters were found for Zr and O atoms, indicating that the distortion produced by \alpha particle-induced localized defects mainly affects the ZrO_{8} unit. The overall shape of SiO_{4} tetrahedra remains essentially undistorted, while Si—O bonds are found to lengthen by 0.43%.
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  • 7
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract The temperature dependence of the lattice parameters of pure anorthite with high Al/Si order reveals the predicted tricritical behaviour of the $$I\bar 1 \leftrightarrow P\bar 1$$ phase transition at T c * =510 K. The spontaneous strain couples to the order parameter Q° as x i∝S xQ i Q°2 with S xQ 1 =4.166×10−3, S xQ 2 =0.771×10−3, S xQ 3 =−7.223×10−3 for the diagonal elements. The temperature dependence of Q° is $$Q^{\text{o}} = \left( {1 - \frac{T}{{510}}} \right)^\beta ,{\text{ }}\beta = \tfrac{{\text{1}}}{{\text{4}}}$$ A strong dependence of T c * , S xQ i and β is predicted for Al/Si disordered anorthite.
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  • 8
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract A theoretical concept is outlined, which links the kinetics of structural transformations with thermodynamic theories of structural phase transitions. Starting from Landau theory and Markovian processes, the general rate laws for crystals with long correlation lengths are derived. The rate laws in Ginzburg-Landau theory are $$1{\text{n }}\Delta Q - 1{\text{n }}f\left( Q \right) \propto - \frac{t}{\tau }{\text{ for }}T \ll T_c {\text{ and }}T \gg T_c$$ and Q 2∝ for T ≈ T c . The physical meaning of the time constant τ and the correction term f(Q) are explained. Fluctuations of the order parameter lead to damping behaviour with explicit dependence on the wavelength of the fluctuation wave and modulation-dependent variations of the lattice strain. Lattice relaxations and activation processes are discussed. Typical rate laws are found to follow $$\begin{gathered} \ln \Delta Q = rln\Delta t, \hfill \\ ln\frac{Q}{Q} + \frac{{1\varepsilon }}{{2k_B T}}\left( {Q^2 - Q_0^2 } \right) = \frac{{\Delta t}}{{\tau *}} \hfill \\ \end{gathered} $$ which leads for short time intervals to a linear rate law $$\Delta Q \propto \Delta t$$ It is shown that linear terms in the Landau potential are equivalent to a logarithmic decay of the excess entropy ΔS ∝ ln Δt which is also expected to be the dominant rate law in field-induced pseudo-spin glasses: $$\Delta Q \propto 1{\text{n }}\Delta t{\text{ and }}1{\text{n}}\left( {\Delta {\text{Q}} \cdot \Delta {\text{t}}} \right) = A{\text{ }}\Delta t + B$$ Fluctuations lead to spatially heterogeneous distributions of the order parameter. A two phase field is found in this case where the nucleation energy is overcome by fluctuation processes. Random fields, arising, for example, from lattice imperfections, lead also to spacially inhomogeneous material. The dominant microstructure is the lattice modulation mostly in the form of a cross hatched pattern (tweed) but also in the form of incommensurate modulations.
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  • 9
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract The lattice parameters of anorthites An98Ab2 and An100 have been measured from 22 to 1100 K. The spontaneous strain arising from the $$I\overline 1 - P\overline 1$$ displacive transition in An98 follows second order Landau behaviour. The spontaneous strain (ɛ s) couples quadratically to the order parameter (Q 0) with ɛ s∝Q 02∝(T c * −T) and T c * =530 K in An98. This is in contrast to the tricritical behaviour observed in pure anorthite. These observations are consistent with a Landau model for the free energy of Ca-rich plagioclases in which Al/Si order and Na content renormalize the fourth order coefficient.
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Physics and chemistry of minerals 16 (1988), S. 298-303 
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract The change from cubic to tetragonal symmetry in natural leucite, KAlSi2O6, involves two types of twinning, which appear sequentially with decreasing temperature: (1) lamellar, associated with the point group symmetry reduction m3m to 4/mmm; (2) merohedric, associated with the change 4/mmm to 4/m. Twin orientations have been deduced from X-ray precession photos and TEM diffraction patterns and images. These are confirmed by theory, using the concept of spontaneous strain and the symmetry relations between adjacent domains. Lamellar twins have boundaries parallel to {101} of the cubic phase, and are cross-cut by the merohedric twins, which have irregular boundaries with x and y in adjacent domains interchanged. On an electron microscopic scale, the distortion arising from twin intersections is revealed by a curvature of one twin wall adjacent to another, and by needle-shaped domains. The macroscopic orientation of the lamellar twins is related to the lattice parameters and hence the magnitude of the spontaneous strain. This in turn leads to the characterisation of the order parameter for the m3m to 4/mmm transformation.
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